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Mesoscopic Quantum Optics

Y. Yamamoto, Ataç İmamoğlu

Published Oct 11, 1999• 194 citations
OpenAlex

Abstract

Basic Concepts. Canonical Quantization. Quantum States of the Electromagnetic Fields. Coherence of the Electromagnetic Fields. Quantum States of Atoms. Interaction between Atoms and Fields. Mathematical Methods for System-Reservoir Interaction. Stochastic Wavefunction Methods. Quantum Nondemolition Measurements. Semiconductor Bloch Equations. Excitons and Polaritons. Coulomb Blockade and Squeezing. Current Noise in Mesoscopic and Macroscopic Conductors. Nonequilibrium Green's Function Formalism. Quantum Statistical Properties of a Laser. Index.

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Basic Concepts. Canonical Quantization. Quantum States of the Electromagnetic Fields. Coherence of the Electromagnetic Fields. Quantum States of Atoms. Interaction between Atoms and Fields. Mathematical Methods for System-Reservoir Interaction. Stochastic Wavefunction Methods. Quantum Nondemolition Measurements. Semiconductor Bloch Equations. Excitons and Polaritons. Coulomb Blockade and Squeezing. Current Noise in Mesoscopic and Macroscopic Conductors. Nonequilibrium Green's Function Formalism. Quantum Statistical Properties of a Laser. Index.
Theory of the interaction between atom and radiation field: three pictures in quantum mechanics description two-level atom and the optical Bloch equation quantized description of the radiation field Dicke Hamiltonian and Jaynes - Cummings model quantum theory of a small system coupling to a reservoir. The quantum properties of light: coherence of light squeezed states of light resonance fluorescence superfluorescence optical bistability effects of virtual photon processes. Quantum properties of the atomic behaviour under the interaction of the radiation field: collapses and revivals of the atomic populations squeezing effects of the atomic operators coherent trapping of the atomic population quantum characteristics of a two-atom system under the interaction of radiation field autoionization of the atom in a laser field motion of the atom in a laser field laser cooling.
Nonequilibrium Green's Functions: History, General Problems, Plasmas: Real-Time Nonequilibrium Green's Functions (L V Keldysh) Theory of High-Tc Superconductivity in Layered Cuprates (A A Abrikosov) Correlated Quantum Plasmas in Strong Laser Fields (M Schlanges et al.) Quantum Transport in Semiconductors: Non-Equilibrium Green's Functions in Semiconductor Device Modeling (R Lake et al.) Nonequilibrium Green Function Modelling of Transport in Mesoscopic Systems (A-P Jauho) Bohm Trajectories in Quantum Transport (J R Barker) Optical and Electronic Properties of Semiconductors: Coulomb Correlations in the Quantum Kinetics of Electron Phonon Systems (W Schafer et al.) Excitonic Quantum Coherences and Correlations in Semiconductor Quantum Wells (R Binder et al.) Nuclear Matter and High Energy Physics: Renormalization of Self-Consistent F-Derivable Approximations (H van Hees & J Knoll) Crossover from Neutron-Proton Superfluidity to Bose-Einstein Condensation of Deuterons in Nuclear Matter (A A Isayev) Kinetics of Vacuum Pair Creation in Strong Electromagnetic Fields (A V Tarakanov et al.) Alternative Computational Methods: Time-Dependent Density Functional Theory from a Practitioners Perspective (K Andrae et al.) Combination of Quantum Kinetic Theory and First-Principle Simulations for Strongly Correlated Quantum Plasmas (M Bonitz et al.) Tunneling of Interacting Identical Particles (Yu E Lozovik et al.) and other papers.
The modified Langevin noise formalism (MLNF) models the interaction of the quantized electromagnetic field with an arbitrary lossy magneto-dielectric object placed in vacuum using three types of non-interacting bosonic polaritons: scattering, electric, and magnetic. These respectively represent free-space photons scattered by the object, and photons radiated by quantized electric and magnetic dipolar sources embedded within its volume. Recently [A. Ciattoni, Phys. Rev. A 110, 013707 (2024)], this formalism was justified from the canonical quantization of macroscopic electromagnetism (CQME) [Philbin, New J. Phys. 12, 123008 (2010)] in the Heisenberg picture. This was achieved by identifying the polariton operators within the formal solution of the macroscopic Maxwell equations, assuming they obey bosonic commutation relations to retrieve the canonical ones, and showing they diagonalize the CQME Hamiltonian. However, the explicit functional dependence of these polaritons on the underlying canonical field operators remained undetermined. In this paper, we derive the exact analytical expressions for the polariton operators in terms of the canonical CQME field operators. Using these mappings, we provide a direct and rigorous derivation of the MLNF from the canonical theory in the Schrödinger picture. Our derivation is structured in three foundational steps: 1) adopting the derived analytical expressions as the constitutive definitions of the polariton operators; 2) mathematically proving that these operators are strictly bosonic as a direct consequence of the canonical commutation relations; and 3) demonstrating that they exactly diagonalize the macroscopic CQME Hamiltonian.
This book provides an elementary introduction to the subject of quantum optics, the study of the quantum mechanical nature of light and its interaction with matter. The presentation is almost entirely concerned with the quantized electromagnetic field. Topics covered include single-mode field quantization in a cavity, quantization of multimode fields, quantum phase, coherent states, quasi-probability distribution in phase space, atom-field interactions, the Jaynes-Cummings model, quantum coherence theory, beam splitters and interferometers, dissipative interactions, nonclassical field states with squeezing etc., 'Schrödinger cat' states, tests of local realism with entangled photons from down-conversion, experimental realizations of cavity quantum electrodynamics, trapped ions, decoherence, and some applications to quantum information processing, particularly quantum cryptography. The book contains many homework problems and an extensive bibliography. This text is designed for upper-level undergraduates taking courses in quantum optics who have already taken a course in quantum mechanics, and for first and second year graduate students.
We study the strong coupling between photons and atoms that can be achieved in an optical nanofiber geometry when the interaction is dispersive. While the Purcell enhancement factor for spontaneous emission into the guided mode does not reach the strong-coupling regime for individual atoms, one can obtain high cooperativity for ensembles of a few thousand atoms due to the tight confinement of the guided modes and constructive interference over the entire chain of trapped atoms. We calculate the dyadic Green's function, which determines the scattering of light by atoms in the presence of the fiber, and thus the phase shift and polarization rotation induced on the guided light by the trapped atoms. The Green's function is related to a full Heisenberg-Langevin treatment of the dispersive response of the quantized field to tensor polarizable atoms. We apply our formalism to quantum nondemolition (QND) measurement of the atoms via polarimetry. We study shot-noise-limited detection of atom number for atoms in a completely mixed spin state and the squeezing of projection noise for atoms in clock states. Compared with squeezing of atomic ensembles in free space, we capitalize on unique features that arise in the nanofiber geometry including anisotropy of both the intensity and polarization of the guided modes. We use a first-principles stochastic master equation to model the squeezing as a function of time in the presence of decoherence due to optical pumping. We find a peak metrological squeezing of $\ensuremath{\sim}5$ dB is achievable with current technology for $\ensuremath{\sim}2500$ atoms trapped 180 nm from the surface of a nanofiber with radius a=225a=225a=225 nm.